bash file check for empty file fails

I need to check if it has data it works correctly if it is empty it fails.

#!/bin/bash
while read _mem
do
  if [[ -s $_mem ]] ; then
    echo "$_mem"
  else
    echo "The file is empty"
  fi
done

I run it like this ./filechk.sh < stuff

If the file stuff has data it prints each line of the file. If it is empty it prints nothing. I think it has something to do with the fact that the read fails so the loop fails but when I change it to this.

#!/bin/bash
while read _mem
do
  if [[ -s $_mem ]] ; then
    echo "$_mem"
  fi
done || echo "The file is empty"

That does not work either as even though the read fails it exits with 0.